Identify the recursive formula for the sequence -3, 9, -27, 81, ....

The inequalities given are 9) "And inequality, 10) "Or" inequality.

Compound inequalities are inequalities which consist of two or more simple inequalities.

"And" compound inequality has both the inequalities true.

"Or" compound inequalities have any one of them as true.

9. |5 + m| < 13

This can be written as,

-13 < 5 + m < 13

-13 - 5 < m < 13 - 5

-18 < m < 8

This is an "and" inequality. Because m can lie between -18 and 8.

10. 4 |y + 6| ≥ 3

|y + 6| ≥ 3/4

-3/4 ≥ y + 6 ≥ 3/4

-3/4 - 6 ≥ y ≥ 3/4 - 6

-6.75 ≥ y ≥ -5.25

The value of y can be either ≤ -6.75 or y ≥ -5.25. y cannot be both.

So this is an "or" inequality.

Hence the first one is and inequality and the second one is or inequality.

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The reason why these triangles are similar is A. AA.

A similar triangle is a triangle in which the corresponding angles are congruent (equal in measure) and the corresponding sides are in proportion. This means that the corresponding sides of two similar triangles are in the same ratio, but the triangles may be different sizes.

A triangle is a three-sided polygon. It is defined by three points in a plane, called its vertices, and the straight lines connecting each pair of these points, called its sides. The three angles of a triangle always add up to 180 degrees.

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Answer:

A. $189.

B. $130.

C. Stephanie's.

D. The Mean.

E. The mean is the average of the data. The Median is just the middle number which doesn't reveal all that much about the data.

Answer:

A.) $189

B.) $145✔️ | *(not $130❌)*

C.) Stephanie's

D.) Median✔️ | *(not "mean"❌)

E.) Because there is an outlier, the median is better representative than the mean.

Round to the nearest tenth , if necessary the value of x is 6.3.

What is right triangle ?

A right triangle is a type of triangle in which one angle is equal to 90 degrees. The side opposite this 90-degree angle is known as the hypotenuse, and the other two sides are known as the legs. The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, applies to all right triangles.

To find the value of x ,

⇒ [tex]\frac{10}{x}=\frac{x}{4}[/tex]

⇒ [tex]x^{2} = 40[/tex]

⇒ x = 6.3

Hence , Round to the nearest tenth , if necessary the value of x is 6.3.

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The the tension in the string is 276 N. Thus, the correct answer is B.

The tension in the string provides the centripetal force needed to keep the ball moving in a circular motion. As the tension in the string increases, the centripetal force increases as well, and the ball will move in a smaller circle (the radius will decrease). Therefore, if the tension increases, the radius decreases and the velocity increases, and if the tension decreases, the radius increases and the velocity decreases.

To determine the tension in the string, we can use the equation:

Where m is the mass of the ball, v is the velocity of the ball, and r is the radius of the circle.

In this problem:

So, tension:

The tension in the string is 276 N. Hence, the correct answer is B.

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Answer:

1) can 2) can’t 3) can’t 4) can

Step-by-step explanation:

There are 66 golf balls in total 1 and 4 are the only equations that equal 66

It is possible that Lance ay that 2,376 ÷10 by the power of 2 i the ame a 2,376 x 0. 1 i he correct

The power (or exponent) of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. In this example the little "2" says to use 8 two times in a multiplication: 82 = 8 × 8 = 64.

What are powers?

A power is the product of multiplying a number by itself. Usually, a power is represented with a base number and an exponent. The base number tells what number is being multiplied. The exponent, a small number written above and to the right of the base number, tells how many times the base number is being multiplied.

Since 2376÷10

It will give us

237.6

So to convert to standard form it will be

2376×10^-1

How

Since the point has been shifted to the right side

And it will definitely give us 2376.0

But the point zero is not necessary

10^1 also means 0.1

So it is possible

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The scale factor of Reggie's drawing is 1/500.

The scale factor of a drawing is the ratio of the size of the drawing to the size of the real object.

To find the scale factor of Reggie's drawing, we can use the information given: in real life, the garage is 3 meters wide, and in the drawing, it is 6 millimetres wide.

We know that:

Scale factor = size of drawing/size of the real object

We can use this equation to find the scale factor of Reggie's drawing:

Scale factor = 6 millimetres / 3 meters

To make the units consistent, we need to convert 3 meters to millimetres.

1 meter = 1000 millimeters

So, 3 meters = 3 * 1000 millimeters = 3000 millimeters

Now we can substitute this value into the scale factor equation:

Scale factor = 6 millimetres / 3000 millimetres

Simplifying the fraction: Scale factor = 1/500

Therefore, the scale factor of Reggie's drawing is 1/500. This means that every 1 millimetre on the drawing represents 500 millimetres (or 0.5 meters) in real life.

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Answer:

2:10 or 1:5

Step-by-step explanation:

Answer: 4 squares to 1 triangle

Step-by-step explanation: both can be divided by two and that is the largest number they can be divided into

If the equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books. The number of books is 4.

Given data:

Equation: 3.95m + 8.95b = 47.65

Where:
Magazine, m = 3

Now let find the number of book by using the equation to solve for b

3.95(3) + 8.95b = 47.65

11.85 + 8.95b = 47.65

Collect like terms

8.95b = 35.8

Divide both side by 8.95b

b = 35.8/8.95

b = 4 books

Therefore we can conclude that the number of books is 4.

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The complete question is;

Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. If Hugh bought 3 magazines, how many books did he buy? The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.

The solution of system of equations are (4, 2). Therefore, option A is the correct answer.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given equation is y=-x+6 ---------(I)

On a coordinate plane, a line goes through (0, 0) and (4, 2).

Here, slope m=(2-0)/(4-0)

= 1/2

Substitute m=1/2 and (4, 2) in y=mx+c, we get

2=1/2 (4)+c

c=0

y=1/2 x ---------(II)

Substitute equation (II) in equation (I), we get

1/2 x=-x+6

x=-2x+12

x+2x=12

3x=12

x=4

Substitute x=4 in equation (II), we get

y=2

Then, solution of system of equations is (4, 2)

Therefore, option A is the correct answer.

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Answer:

9 yards is a better estimate.

Step-by-step explanation:

This is because it is closer to the actual answer. 9 yards is only 1 foot off while the other is 2.

y = 8450(0.7640)ˣ is the equation that will model this situation

The general form of exponential equation is given by:

y = abˣ

Where a is the initial value of the car, b is the depreciation rate and x is the number of years

When x = 0, y = $8450:

y = abˣ

8450 = ab⁰

a = 8450

In 1993, x = 1993 - 1988 = 5 years and y = $2200:

y = abˣ

2200 = 8450b⁵

b⁵ = 2200/8450

b = [tex]\sqrt[5]{}[/tex](2200/8450)

b = 0.7640

Thus, the equation that model the situation is y = 8450(0.7640)ˣ

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Answer:

the first and the third

Step-by-step explanation:

The required point is 0.25 miles away from the nearest point on the shore.

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) =  lim h--> 0 (f(x + h) - f(x)) /(x + h - x).

here, we have,

It can be applied to minimize or maximize a function.

The given problem can be shown in the form of a diagram as follows

Suppose the underwater cable meet the shore at a distance x from the nearest point.

Then, the distance of cable in water is x² + 3.5² = x² + 12.25

And, the distance of cable in the ground is 10 - x.

As per the question, the cost of the laying cable can be represented as follows,

C(x) = 1200(10 - x) + 2400(x² + 12.25)

In order to minimize the cost the above function can be differentiated and equated to zero as,

C'(x) = -1200 + 4800x = 0

=> x = 1200/4800

      = 1/4

      = 0.25

Hence, in order to minimize the cost of the entire project the underwater cable should meet the shore at 0.25 miles away from the nearest point.

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Answer:  42

Step-by-step explanation:

Math

Answer: D

Step-by-step explanation:

Answer:

D) 320 pi

Step-by-step explanation:

pi*r^2*h is the equation for the volume of a cylinder.

If you plug in the given values, then you get 320pi.

The answer is D) 320 pi.

Hope this helped! :)

Answer:

3 inches

Step-by-step explanation:

The perimeter is the sum of all the sides of a shape. A rectangle has 4 sides.

2 * 2 = 4

One side is 2 in., so the parallel side is also 2 in.

10 - 4 = 6

Subtract the sum from the perimeter.

6 / 2 = 3

Since there are two sides left, divide by 2.

A quadrilateral shape called a trapezoid that has exactly one set of parallel sides. Isosceles Trapezoid: A trapezoid with congruent non-parallel sides.

A quadrilateral is a polygon with four vertices, four sides, and four angles, all of which add up to 360 degrees. The quadrilateral is formed by two triangles when the diagonals are drawn. The angle total for these two triangles is 180°. As a result, the quadrilateral has a 360° total angle.

With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. A quadrilateral's internal angles add up to 360 degrees in all cases. The four angles found at each vertex of a four-sided form are referred to as the interior angles of a quadrilateral and are the only angles in a quadrilateral. Every quadrilateral's internal angles add up to 360 degrees.

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So on solving the provided question we can say that -  all angles of triangle - 180; x = 60

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

all angles of 180

x +90+30 = 180

x = 60

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The value of x is 0.01

Angles can be measured using one of two standard units. Degrees are the most widely used unit of measurement. A straight angle is 90° since a circle has 360 equal degrees. We'll just take into account angles between 0° and 360° for the time being; however, we'll take into account angles higher than 360° and negative angles later, in the section on trigonometric functions.

Minutes and seconds can be used to further split degrees, but this separation is less common than it once was. Minutes are the 60 equal pieces that make up each degree. Thus, seven and a half degrees can also be written as seven degrees and thirty minutes, or seven°30'. Additionally, each minute is divided into 60 equal seconds.

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The length of the side indicated in the similar figure can be found using the concept of similarity.

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The volume of a box shape of a right rectangular prism with height 10 inches, length 7 inches, and width 4 inches would be 280 cubic inches.

Volume can be defined as the amount of space occupied by any three-dimensional solid. These solids can be anything from a cube to a cuboid, a cone, a cylinder or a sphere.

It is also the measure of the capacity that an object holds.

Volume = h x l x w

where

h = 10 inches

l = 7 inches

w = 4 inches

Volume = 10 x 7 x 4

Volume = 280 cubic meters

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The value of x is 6.2 units.

Now by using the Pythagorean theorem

Hypotenuse² =  Perpendicular² + Base²

Now in the Δ ABD

As given DB² = DA² + AB²

As given

DB = 13 units

AB = 9 units

Putting values in the above

13² = 9²+ DA²

169 - 81 = DA²

88 = DA²

DA=√88

In ΔABC

AB² = AC² + CB²

(As given AB = 9 units , CB = x)

9² = AC² + x²

AC ² = 81 - x²

Now in ΔADC.

AD² = AC² + DC ²

As AC ² = 81 - x²

DC = 13 - x

AD=√88

(√88)²=81-x²+(13-x)²

(By using the formula (a + b)² = a² + b² + 2ab )

88=81-x²+13²-2*13*x+x²

88=81-x²+13²-26x+x²

88-81 - 169 = -26x

88-250 =-26x

-162 = - 26x

x=162/26

x = 6.2 (Approx)

Therefore the value of x is 6.2 units.

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The quadrilateral MNPQ is trapezoid but not an isosceles trapezoid .

A trapezoid, as well known as a trapezium, is a closed, flat shape with four straight sides and one pair of parallel sides.

Here given points,

M(-2,0), N(0,4), P(5,4), and Q(8,0) are given.

We are familiar with the slope formula,

Slope = y2 - y1 / x2 - x1

So here,

Slope of MN = 4 - 0 / 0 - (-2)

                     = 4/2

                     = 2

Slope of NP = 4 - 4 / 5 - 0

                     = 0/5        

                     = 0

Slope of PQ = 0 - 4 / 8 - 5

                     = -4/3

Slope of QM = 0 - 0 / -2 -(-8)

                     = 0/10

                     = 0

Therefore we can see, NP||QM and MN∦PQ.

Therefore MNPQ is a trapezoid because it has two parallel sides.

By using distance formula,

MN = [tex]\sqrt{0-(-2)^{2} +(4-0)^{2} }[/tex]

      = √20

      = 2√5 units

PQ = [tex]\sqrt{(8-5)^{2} +(0-4)^{2} }[/tex]

      = √25

      = 5 units

Here MN ≠ PQ , MN and PQ are not congruent to each other.

Therefore MNPQ not is a isosceles trapezoid.

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Therefore , equation problem answer is there will be six 5 mark problem and twenty two 3 mark problem.

Remove parentheses from each side of the equation and combine similar terms to make it simpler. To separate the variable term on one side of the equation, use addition or subtraction. To find the variable, use division or multiplication.

Here,

Given :

Since the total number of points is 28, we can create the Let Statements:

Let x= one type of question

Let 28-x= the other type of questions

Create an equation to relate the number of questions to the price

100=5x+3(28-x) Distribute

100=5x+82-3x Subtract 76 from both sides of the equation

100-82=5x-3x Combine like terms

18=3x Divide both sides by 3

x=6

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A description which best compares the graphs of the two functions above include the following: B. The line for function A is steeper.

In order to compare the two functions, we would have to find the slope of function B based on the data points contained in the table by using the slope formula.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have the following;

Slope, m = (-1 - (-2))/(3 - 0)

Slope, m = (-1 + 2)/3

Slope, m =1/3

From function A y = 3x - 2, the slope is equal to 3. Consequently, we can logically deduce that the line representing function A is steeper than the line representing function B because its slope is bigger i.e 3 > 1/3.

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To convert from base 10 to base e, we need to split down a number in base e into the powers of e.

When we convert from base 10 to base e, the pattern will be exactly the same. It will be just with e instead of 10.

For example, to see how many digits (before the decimal point) of ln(12) = 2.4849...

It means that the first digit will be on the e^2 position. Now lets find:

12 / e^2 = 1.624…

So, there will only be a 1 in the e^2 position. The remaining is 12 – e^2. The next position is e^1 position. To find out what’s on this position, we need to do the following calculation:

(12 – e^2) / e = 1.696…

The next digit will also be a 1.

Now we do the 1’s position:

(12 – e^2 – e) / 1 = 1.892…

Next digit’s a 1.

We can continue for a few more decimal places:

(12 – e^2 – e – 1) / e – 1 = 2.426…

Next digit’s a 2.

(12 – e^2 – e – 1 – 2 * e – 1) / e – 2 = 1.159…

Next’s digit a 1.

So, 12 in base e is 111.21…

Since e is irrational and 12 is not, this will be never ending. But there will only can be 0’s, 1’s, and 2’s, since e is less than 3.

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Answer:

The correct answer is A

I hope that helped.

Step-by-step explanation:

The distance between the 7th seconds and the 10th seconds is  29.4 m.

It is arithmetic.

An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is always the same, called the common difference.

Since the height in the 1st second, 2nd second and 3rd second are 4.9m, 14.7 and 24.5 respectively.

They have a common difference (d) of 9.8. That is:

d = 14.7 - 4.9 = 9.8  

Thus, it is arithmetic

The formula for determining nth of an AP is given by:

nth = a + (n-1)d

where a is the first term, d is the common difference and n is the number of terms

7th seconds:

nth = a + (n-1)d

nth = 4.9 + (7-1)9.8 = 63.7 m

10th seconds:

nth = a + (n-1)d

nth = 4.9 + (10-1)9.8 = 93.1 m

distance between the 7th and the 10th seconds:

10th seconds - 7th seconds = 93.1 - 63.7 = 29.4 m

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